Water conducts electricity, which is why it is so dangerous to mix water and power points, and why a hairdryer in the bath is lethal. Water and electricity, the classic deadly pair. Water is a conductor, full stop.
Pure water is actually a poor conductor of electricity. What conducts is not the water itself but the stuff dissolved in it: minerals, salts, and other ions that carry charge through the liquid. Truly pure, distilled, deionised water is a surprisingly good insulator, which is why it is used in some sensitive electronics. The catch, and it is a big one, is that essentially no water you will ever meet is pure. Tap water, rain, river water, seawater, the water on your skin, and the water in your bath are all loaded with dissolved ions, so they conduct electricity very well and absolutely will kill you with a hairdryer. So the safety message is completely correct, even though the science behind it is usually stated wrong. The danger is real because real-world water is full of impurities. It is just not the H2O doing the conducting. Stay terrified of water near electricity; the impurities have earned that fear.